Linear vs Nonlinear

Front

What is a linear equation?

Back

An equation that graphs to a straight line, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a nonlinear equation?

Back

An equation that does not graph to a straight line, which can include curves, circles, or other shapes.

Front

How can you identify a linear relationship from a graph?

Back

A linear relationship will show a straight line when plotted on a graph.

Front

How can you identify a nonlinear relationship from a graph?

Back

A nonlinear relationship will show a curve or any shape that is not a straight line when plotted on a graph.

Front

What is the slope in a linear equation?

Back

The slope (m) represents the rate of change of the dependent variable (y) with respect to the independent variable (x).

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept (b) is the point where the line crosses the y-axis, indicating the value of y when x is 0.

Front

What is an example of a linear function?

Back

y = 2x + 3 is a linear function.

Front

What is an example of a nonlinear function?

Back

y = x^2 is a nonlinear function.

Front

What does it mean if a function is linear?

Back

It means that the function has a constant rate of change and can be represented by a straight line.

Front

What does it mean if a function is nonlinear?

Back

It means that the function has a variable rate of change and cannot be represented by a straight line.